On the Poincaré-Lyapunov constants and the Poincare series

Jaume Giné, and Xavier Santallusia. "On the Poincaré-Lyapunov constants and the Poincare series." Applicationes Mathematicae 28.1 (2001): 17-30. <http://eudml.org/doc/279485>.

@article{JaumeGiné2001,
abstract = {For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial differential systems.},
author = {Jaume Giné, Xavier Santallusia},
journal = {Applicationes Mathematicae},
keywords = {Poincaré-Lyapunov constants; Poincaré series; center focus problem; nonlinear differential equations},
language = {eng},
number = {1},
pages = {17-30},
title = {On the Poincaré-Lyapunov constants and the Poincare series},
url = {http://eudml.org/doc/279485},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Jaume Giné
AU - Xavier Santallusia
TI - On the Poincaré-Lyapunov constants and the Poincare series
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 1
SP - 17
EP - 30
AB - For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial differential systems.
LA - eng
KW - Poincaré-Lyapunov constants; Poincaré series; center focus problem; nonlinear differential equations
UR - http://eudml.org/doc/279485
ER -